Fractional iteration and functional equations for functions analytic in the unit disk

DOI10.1007/BF03321854zbMath1062.30026OpenAlexW2000339201MaRDI QIDQ1880907

Simeon Reich, Mark Elin, Viktor V. Goryainov, David M. Shoikhet

Publication date: 27 September 2004

Published in: Computational Methods and Function Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf03321854

zbMATH Keywords

functional equationinfinitesimal generatorembeddabilityKœnigs functionfractional iterationsemigroup of analyitc functions

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Iteration theory, iterative and composite equations (39B12) Functional equations for complex functions (39B32)

Related Items (9)

Semiflows, composition semigroups, and the approximation of Dirichlet-to-Neumann semigroups ⋮ On Ulam stability of the inhomogeneous version of the general linear functional equation ⋮ Value regions of univalent self-maps with two boundary fixed points ⋮ Angular and unrestricted limits of one-parameter semigroups in the unit disk ⋮ A flower structure of backward flow invariant domains for semigroups ⋮ Infinitesimal generators associated with semigroups of linear fractional maps ⋮ On fractional iterates of a Brouwer homeomorphism embeddable in a flow ⋮ Kœnigs-type linearization models and asymptotic behavior of one-parameter semigroups ⋮ Dirichlet-to-Robin operators via composition semigroups

Cites Work

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• Semigroups of analytic functions and composition operators
• Schröder's functional equation and the Koenigs embedding property.
• Iteration and the Solution of Functional Equations for Functions Analytic In the Unit Disk
• Estimates of the extinction probability of the Galton-Watson process
• Fractional iteration near a fixpoint of multiplier 1.
• Embedding Iterates of Analytic Functions with Two Fixed Points into Continuous Groups
• Two works on iteration and related questions

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